Question

Why is angular momentum conserved in a satellite?

Answer 1

The principle of conservation of momentum, both linear (also known as translational) and angular, is a universal principle of Physics.

Explanation:

Angular momentum, `L`, is defined, in mathematical terms as

`L = I*omega`

Take the time derivative of that

`(dL)/dt = I*(domega)/dt`

We give the term "torque" to `I*(domega)/dt` and we give torque the variable name `tau`.
We give `(domega)/dt` the variable name `alpha`.

Expanding that last equation with the variable names `alpha and tau`

`(dL)/dt = I*(domega)/dt = I*alpha = tau` ... Equation1

The equation `tau = I*alpha` is the angular equivalent of `F = m*a` which Newton made famous in Newton's 2nd Law.

`tau, I, and alpha` are the angular equivalents of `F, m, and a` respectively.

If there are no external torques acting on a body, `tau = 0`, and that there is no angular acceleration follows. That is shown in the repeat of Equation 1 below.

`(dL)/dt = I*(domega)/dt = I*alpha = 0`

Therefore `(dL)/dt = 0`. And therefore, the angular momentum is constant if `tau = 0`.

Therefore, we have Conservation of Angular Momentum .

I hope this helps,
Steve